论文标题
多元纵向数据的协方差矩阵的贝叶斯半参数建模
Bayesian semiparametric modelling of covariance matrices for multivariate longitudinal data
论文作者
论文摘要
本文开发了用于多元纵向响应的边际模型。总体而言，该模型由五个回归键组成，一个用于平均值，四个用于协方差矩阵，后者是通过考虑各种矩阵分解而产生的。我们采用的分解是直观的，易于理解的，它们不依赖于任何假设，例如在多元响应之间存在订购。回归的子模型是半参数，其功能未知以基础函数扩展为代表。我们使用Spike-Slap先验进行回归系数来实现可变选择和函数正则化，并获得有关模型不确定性的参数估计。开发了一种有效的马尔可夫链蒙特卡洛算法，用于后采样。仿真研究提出了研究先验对后代的影响，这是人们在考虑进行多元纵向分析而不是单变量分析时可能带来的收益，以及这些收益是否可以抵消丢失数据的负面影响。我们将方法应用于高度不平衡的纵向数据集，并在20年内观察到四个响应
The article develops marginal models for multivariate longitudinal responses. Overall, the model consists of five regression submodels, one for the mean and four for the covariance matrix, with the latter resulting by considering various matrix decompositions. The decompositions that we employ are intuitive, easy to understand, and they do not rely on any assumptions such as the presence of an ordering among the multivariate responses. The regression submodels are semiparametric, with unknown functions represented by basis function expansions. We use spike-slap priors for the regression coefficients to achieve variable selection and function regularization, and to obtain parameter estimates that account for model uncertainty. An efficient Markov chain Monte Carlo algorithm for posterior sampling is developed. The simulation studies presented investigate the effects of priors on posteriors, the gains that one may have when considering multivariate longitudinal analyses instead of univariate ones, and whether these gains can counteract the negative effects of missing data. We apply the methods on a highly unbalanced longitudinal dataset with four responses observed over of period of 20 years
